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U. S. LIGHT-HOUSE ESTABLISHMENT. 


MEMOIR 

UPON THE STABILITY 


OF TIIE 


LIGHT-HOUSE IN COURSE OF CONSTRUCTION 

AT 


BELLE ISLE. 



BY LEONOR FRESNEL, 

A t\ 

ENGINEER IN CHIEF OF THE ROYAL CORPS “ DES FONTS ET CHAUSEES,” SECRETARY 
OF THE COMMISSION OF LIGHT-HOUSES. 


Extracted from the “ Annales des ponts et cbaus^es,” and published in Paris in 1832. 

Translated by direction of the Light-house Board for the use of the officers connected with 
the light-house service of the United States. 


WASHINGTON: 

WILLIAM A. HARRIS, PUBLIC PRINTER. 

1858 . 


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MEMOIR 


UPON THE STABILITY 

OP THE 

LIGHT-HOUSE IN COURSE OF CONSTRUCTION 

AT 

BELLE ISLE. 


The project proposed in 1825 by Augustine Fresnel, my brother, 
for the light-house of Belle Isle, and approved in 1827, has appeared 
to the engineers charged with its execution, to need divers modifica¬ 
tions designed to increase the stability of this edifice against the 
action of the winds. These engineers have presented several memoirs 
on this subject, which have been submitted to the commission of 
light-houses, and to the general council of bridges and roads. I will 
not attempt here to offer a complete analysis of the discussions of 
which these memoirs have been the object, as it would embrace a 
great many details of an entirely local interest. In determining to 
treat anew the questions relating to the stability of the Belle Isle 
light-house, I have thought that I ought to disengage them as much 
as possible from all discussion of specialities, in order to consider them 
only in such relations as have appeared of a nature to interest con¬ 
structors. In this view, I have kept myself closely to the facts, seek¬ 
ing information from experience by different comparisons between the 
light-house in question and several edifices of the same kind. I will 
urge those comparisons in which I have taken successively for objects. 
(See Plate.') 

The signal tower of L’ Orient, fig. 1. 

The great light-house of Genoa, fig. 2. 

The light-house of the Pilier, near the island of Noirmoutier, fig. 4. 

The Planier light house, near Marseilles, fig. 5. 

The column of Boulogne-sur-mer, fig 6. 

The chimney of the salt refinery of the village of Ars, isle of fie, fig. 7. 

The chimney of the forges of Alais, fig. 8. 

The chimney of the steam engine of the dock of St. Ouen, near Paris, fig. 9. 

The chimney of the gas works of the Faubourg Montmartre, fig. 10. 



4 


But before entering into tlie details relating to tbe composition and 
stability of these different towers, I must present some general consider¬ 
ations upon the action of the winds, and show briefly the principles 
which have served as the basis of my calculations. 

It appears that hitherto but little attention has been paid to the 
determination of the limit of the pressure exerted by the wind against 
edifices. It would seem, however, that this research ought to have 
fixed the attention of architects who rival each other in boldness in 
the construction of the high chimneys of forges and steam engines. 
It is true, that in our climate we rarely have examples of edifices of 
masonry overturned by the wind, and that the damages which occur 
proceed more commonly from some faults in the construction. How¬ 
ever, it must be acknowledged that the effort of the wind acting upon 
works of masonry, still new and with little homogeneousness, has, 
under certain circumstances, determined or hastened their destruction, 
by causing or increasing unequal settling. It is then interesting, 
under several aspects, to study this action, and to appreciate its 
effects. 

We know that all towers isolated, and of rather a light construc¬ 
tion, experience in tempests oscillations analogous to the swaying oj 
trees. These oscillations evidently result from the elasticity of the 
body of the edifice and the intermission of the wind. Those which 
I have had occasion to observe have appeared to me to succeed each 
other at intervals of one or two seconds. Besides, they were not 
accompanied by any of those tremors or rapid vibrations which the 
shock of a hard body, or of the waves, could have produced. I will 
add, that an attentive examination of several high towers exposed to 
frequent gales, has not enabled me to discover any trace of damage 
which could be attributed to these oscillations. Some constructed 
nearly wholly of rubble, and covered with a layer of mortar, like those 
of Genoa and L’Orient; others constructed of cut stone, like the tower 
of Corduan, and the column of Boulogne, have shown no horizontal 
fissure either in the mortar covering or in the joints. Hence, we 
must conclude that their oscillations have caused no permanent de¬ 
rangement in their elements, for, however small such an effect may 
have been, it could not have been manifested at every storm without 
involving the ruin of an edifice exposed for three centuries, like 
the tower of Genoa, to the sudden tempests of the coasts of the 
Mediterranean. 


5 


It must be acknowledged in the second place, that the amplitude 
of these oscillations has been inconsiderable in proportion to the 
height of the towers, since the inflexion has not been great enough to 
form visible fissures. Besides, it is easy to conceive how the total 
resulting effect of the pressure of the wind may become sensible at 
the top of an edifice, and the elimentary efforts not be appreciable. 
But, admitting this assimilation of high towers to elastic rods subject 
to a pressure distributed over their whole length, it may be asked 
why these edifices by virtue of their elasticity are not subject at inter¬ 
vals to destructive vibrations caused by the sudden stoppages of the 
winds which characterize storms ? To this it may be answered, that 
the instantaneousness of these stoppages or changes in the direction 
of the wind is far from being absolute. The elasticity of the air is, 
in fact, incompatible with such a phenomenon, and hence it cannot 
be supposed that the wind, blowing even in sudden tempests, can act 
upon edifices submitted to its effort in the same manner as would a 
solid body or incompressible liquid from which they might receive 
shocks. In fine, all well observed facts appear to demonstrate that 
the oscillations impressed by tempests on masonry towers cannot in¬ 
jure these edifices if they are properly built, unless they are wanting 
in stability—that is, unless they could be overturned in mass by the 
effort of the wind. 

We know that the effort exerted by the wind upon an immovable 
body is the sum of two pressures—one, the resultant of the direct 
action of the air upon the face against which it impinges, the other, 
due to the rarification of this fluid upon the opposite face. Now, 
according to an experiment reported by Smeaton, and cited by M. 
Hachette in his treatise on machines, a plane surface, having an area 
of one square foot, placed perpendicular to the direction of a wind, the 
velocity of which is twenty feet per second, experiences a total pres¬ 
sure equivalent to one pound. The designer of the Belle Isle light¬ 
house, admitting this fact, has also taken as the limit of the greatest 
velocity of the wind 164 feet per second, which exceeds by one-ninth 
the velocity of the greatest storms mentioned in the annual of the 
bureau of longitudes. (Year 1818.) By the help of these constants, 
and supposing the total pressures proportion'll to the squares of the 
velocities, he has been led to estimate the total pressure corresponding 
to a velocity of 164 feet per second at 507 lbs. per superficial yard. 


6 


The results of experiments analyzed by M. Navier in his notes on 
the hydraulic architecture of Belidor, lead to a result a little differ¬ 
ent from this. (1 ) I have thought consequently that I might attach it 
to my calculations, more particularly as I have considered the dis¬ 
cussion of absolute stability as merely a secondary object. 

In order to apply this constant to the determination of the stability 
of a monolithic tower having the form of a right prism with a square 
base, we must multiply the area of one of its faces in square yards by 
507 lbs., and this product multiplied by the semi-height of the prism 
will give the moment of the effort of the wind. We also obtain the 
moment of the resistance, by multiplying the total weight of the 
tower by the half breadth of the base. Dividing this second moment 
by the first, we will obtain the expression for the absolute stability of 
the edifice with respect to the action of the wind. 

In this estimate we do not take account of the diminution of resist¬ 
ance arising from the flexure of the tower, but in addition to the 
want of the constants necessary to determine the deviation of the sum- 

(1) The resistance of an immovable body plunged in a fluid in motion, may be represented 
by the formula S D h (m -)- q) in which S represents the area of the surface acted upon, D 
the weight of a cubic yard of the fluid, h the height due to the velocity of the fluid in 
yards, and m -f- q a co-efficient whose first term depends on the pressure exercised upon 
the front surface of the body, and whose second term q answers to the negative pressure 
upon the opposite face. 

Experience having demonstrated that the co-efficient m -f- q varies with the form and 
dimensions of the body, it can only be determined with some exactness for each applica¬ 
tion from results obtained in analogous circumstances. Among the different experiments 
of Dubuat, we may admit as applicable to square edifices that which concerns the action 
of a fluid upon a cube, and according to which we have m -\- q—\. 457. 

I will suppose the air at the temperature of melting ice, when the weight of a cubic yard 
is 2. 1919 lbs. 

I believe that I thus take an extreme case, for I do not think that in our climate we 
ever have very violent storms at a temperature below 32° Fahrenheit. 

The height h due to a velocity of 164 feet, being also 139 yards, we will have for the 
total pressure per square yard, calculated without regarding the compressibility of the air : 

lbs 2. 1919 X 1. 457 X 139 = 444 lbs. 

But according to an experiment of Hutton, cited by M. Navier, this result ought to be 
augmented about one-sixth on account of the increase of the density of the air by the 
effect of the resistance. We will then have 

P = 518 lbs. 

a total pressure which only differs one-forty-sixth (^) from that indicated by A. Fresnel. 

(See the Principles of Hydraulics, by Dubuat, the Notes of M. Navier upon the Hydraulic Archi¬ 
tecture of Belidor, and the Work of M. Coriolis upon Machines.) 


7 


mit, it is evident that it can he left out of consideration without 
altering the relations which are the essential object of this memoir. 

The square monolithic tower that I have just taken for an example, 
offers the simplest case of calculations of this kind, both on account of 
its shape and the disposition of the plane of rupture. Ordinarily we 
have to consider edifices composed of numerous layers of masonry 
■whose adhesion has the greater influence upon the stability as the sizes 
of the materials entering into the construction are smaller. If we 
suppose this adhesion zero in a tower formed of layers sub-divided 
into brick headers and stretchers, rupture under the effort of the wind 
ought not to take place horizontally. It should take place, as in 
sustaining walls, along an oblique section whose inclination would 
be determined by the condition that the ratio between the effort of the 
wind and the moment of the weight of the solid above this section, 
should be a maximum. But we may observe that in the majority af 
high towers, the adhesion of the mortar and the disposition of the 
materials are such that the section of rupture must be less inclined 
than it is in common sustaining walls. We add, that the results of 
the comparisons between the different edifices previously cited, will 
not be sensibly affected by the hypothesis that the sections of rupture 
are horizontal. We may, therefore, without inconvenience, admit 
this hypothesis, which averts a useless complication of calculations. 

The determination of the point of most easy rupture presents again 
a problem of minima, the direct solution of which would generally 
exact very long calculations ; (2) but fortunately the position of this 

(2) Let us take for example a tower of homogeneous construction, having an outside 
truncated conical surface, and an inside cylindrical open space with the same vertical axis 
as the outside surface. 

Call a the radius of the base of the inside cylinder ; 
b the thickness of the top course ; 
n the slope per unit of the exterior profile ; 

x the vertical distance from the plane of rupture to the top of the tower ; 
r the radius of the section corresponding to the plane of rupture ; 
h the distance of the centre of pressure above the plane of rupture. 

For the present investigation, we may, in the expression for the stability, leave out th e 
constant co-efficient which is the ratio of the weight of a cubic yard of masonry, and the 
weight representing the reduced pressure exercised by the wind upon a square yard of the 
conical surface measured on its vertical projection. Then the three quantities representing 
the moments of the resistance, of the pressure, and the absolute stability, will be replaced 
by the following, viz : 


8 


point in the majority of cases will he manifested at the first glance, 
so that it can easily be determined by a few trials of false positions. 

If we wish to apply these principles to the calculation of the stabi¬ 
lity of a round tower, we find ourselves arrested at once by the diffi¬ 
culty of appreciating the effort exerted by the wind upon the surface 
of a cylinder. In the absence of empirical formulas based upon suffi¬ 
ciently numerous experiments, I have considered one of the element¬ 
ary pressures acting upon the front face of the cylinder, and I have 
determined by a double decomposition along the tangent to the cir¬ 
cular section, and along the diameter perpendicular to the direction 
of the wind, the value of the component tending to overturn the 
obstacle. I have thus been led to admit that the action of the wind 


The first, by the product R of the volume V of the masonry multiplied by the radius r of 
the section of rupture. 

<The second, by the product P of a meridian section of the tower, by the ordinate h of 
the centre of pressure. 

The third, by the quotient S of the first divided by the second. 

Making, in order to simplify the notation— 

a -(- b = p, and 2a -j- b rr q, we will have: 

S _R_ _Vr_ 

P h (2 a + 2 b -J- nz) x 

ir [3 b p q -{- 3 (j3 a -}- b q) nz -f- 4 p n~ z~ -f- n a x 3 ] 

3 pz -j - nz' 2 

h being equal to — (\ 4--- ^ ^ 

3 \ 2 a -f- 2 b -(- nz) 


W hence we deduce the following equation corresponding to the minimum value of S : 

*4 + 6 _z x 3 + 3 JLp l- b ^ x * - Mpj x _v±p*j = 0 . (A) 


To apply this to the determination of the plane of rupture of the tower of Belle Isle, I 
will suppose this edifice freed from its outside basement work, from its staircase, its interior 
arches, its capital, its lantern, and from the parapet wall under the lantern. Hence we 
shall have from Fig. 3— 

a — 2. 296 yds. b— .710 yd. n — .0171 a + b z=p = 3 yds. 2 a + 6 = g — 5. 3 yds. 

- = 58. 3. 
n 


These values substituted in equation, (A,) give 

z 4 + 1049 x 3 -f 236940 x 2 — 13421850 x — 3521187745 = 0. 

From which we obtain x 117 yds. 

Hence we may conclude that the plane of rupture would descend to the level of the 
foundation, if the outside basement work were suppressed. 







9 


upon a vertical cylinder is reduced to two-thirds of that which it 
would exercise upon the meridian section of the same cylinder. ( 3) 

This result, the degree of approximation of which can only he 
determined by some direct experiments, I have used to compare the 
stability of the round tower of the Belle Isle lighjt-house with that 
of the square tower of the Genoa light-house, of the chimneys of the 
salt refinery of Ars, of the steam engine of the dock of St. Ouen, and 
of the gas factory of the Faubourg Montmartre. 

Comparisons of this kind present, I must confess, several causes of 
uncertainty ; hut fortunately we can avoid all difficulty, by only com¬ 
paring edifices which have nearly the same form, and which do not 
present too great differences in their principal dimensions. Thus we 
will compare the cylindrical tower of Belle Isle with a circular edi¬ 
fice like the light-house of the Pilier, the column of Boulogne, or the 
chimney of the forges of Alais ; and the square tower of Genoa will he 
compared with the quadrangular towers of the dock of St. Ouen, or of 
the gas factory of the Faubourg Montmartre. 

Without pressing further these preliminary considerations, which 
appear to me to suffice for the applications which I have had specially 
in view, I pass to the calculation of the stabilities of the different 

(3) Call / the force of the wind ; 

r the radius of the cylinder ; 

a the angle formed by the direction of the wind with the meridian plane cor¬ 
responding to the point of application of the force f. 

The double decomposition spoken of above will give for the value of the component of 
f tending to overturn the cylinder— 


/ cos 2 a dx — 


f dx _ f (r 2 — x 2 ) dx 

1 -(- dyV r 3 

dx 2 


and integrating this expression between the limits x — r, and x — — r we shall have for 
the total pressure upon the semi-cylinder exposed to the wind— 



a value about one-sixth below that which the author of the design of the Belle Isle light¬ 
house used to obtain the results contained upon the second sheet of the lithographic 
plates of that design. 

It seems to result from some experiments of Bossut upon cylindrical prows, that the 
pressure of the wind upon a cylinder would only be one-half of what it would be on a 
meridian section ; but I have not thought that I ought to avail myself of this value, as it 
is too remote from the hypothesis admitted by the author of the design. 

L. II.—2 




10 


edifices previously mentioned, commencing with the Belle Isle 
light-house. 

Belle Isle light-liouse. (Fig. 3.) 

According to the design originally adopted in 1825, the tower of 
Belle Isle light-house was to he constructed as a hollow column 
172.24 feet in height, with an exterior diameter of 23.95 feet at the 
base reduced to 18.04 feet at the top. Its interior diameter was 
fixed at 13.78 feet. The lower part of this column was to be sur¬ 
rounded for a vertical height of 31.16 feet with a circular outside 
basement, with two stories, and 45.92 feet in diameter. The exterior 
wall of this basement was joined to the column by six partition 
walls.* 

Two arched chambers, comprising together a total height of 26.25 
feet, occupied the upper part of the tower. Its platform was sur¬ 
mounted by a cylindrical parapet wall 7.22 feet high and 13.12 feet 
exterior diameter, designed to receive a lantern 11.48 feet in diameter, 
and 9.84 feet high, a dome nearly hemispherical not included. 

Between the entrance story and the first chamber at the top of the 
tower, there was to be an open-work circular staircase, having a cir¬ 
cular well 7.22 feet in diameter. 

The whole of the masonry was to be of cut granite, except the 
foundation, designed to be of rough blocks, and some arches to be of 
brick. 

The mortar was to be made of the common lime of Nantes. 

It was known that at a short distance below the surface of the 
ground from several points examined, a schistose rock was present 
upon which the foundations of the most elevated edifice might be 
safely placed, particularly on the site finally adopted, which is ele¬ 
vated more than 125 feet above the level of high water. 

Since its approval, this design has been several times brought to 
the notice of the council des ponts et chaussees on account of several 
modifications instigated (provoquees) successively by the engineers 
charged with the direction of the work. 

° The principal arrangements of this basement have been suggested to the author of the 
design by M. Tarbd de Vaux-Clairs, Inspector-General des Ponts et chaussees, member of 
the commission of light-houses. 


11 


These modifications consist of— 

1. The addition of a partition wall to the large open circular staircase. 

2. The addition of six large exterior counterforts. 

3. The addition of a mass of masonry about 5.6 feet thick below the helicoidal solid 
formed by the staircase. 

4. The employment of iron cramps to join the stones of each course to each other. 

The increase of expense resulting from these modifications, was to be about forty 

thousand dollars. 

It is essential to observe, that in all this, the only question was to 
obviate presumed dangers, and not to remedy known damages ; for 
at the date when the last modifications proposed were examined, 
(July 1831,) the works executed at the Belle Isle light-house had 
only reached a height of about 23 feet above the entrance story. 

The addition of the partition wall was designed less to consolidate 
the tower, than to consolidate the winding staircase, and to render 
its construction easier. 

It is from this point of view, at least, that the question was viewed 
by the general council “ des ponts et chaussees,” when it adopted 
this modification. The thickness of the partition wall, at first fixed 
at 0.98 feet, was in the end increased to 1.97 feet, in conformity with 
a report of M. Lamblardie, Division Inspector. 

As to the employment of counterforts, and the increased thickness 
of the inclined mass of the staircase, these modifications were pro¬ 
posed only to increase the stability of the projected tower, so that it 
should at least equal that of the signal tower of 1/Orient. This last 
term of comparison had particularly attracted the attention of the 
engineers of the Belle Isle light-house. In fact they considered the 
tower of L’Orient as one of the boldest edifices among all those which 
exist upon our ocean coasts, at least in localities similar to that of 
Belle Isle, with respect to the violence of the winds to which they are 
exposed. 

The employment of full counterforts is generally of little advan¬ 
tage as a means of increasing the resistance of a tower against the 
action of the wind, whilst the additional masonry presents a great 
surface in proportion to its mass; but it must be remembered that the 
works already executed at the Belle Isle light-house permitted no 
other method of obtaining the degree of stability considered necessary, 
for a large increase of the exterior diameter of the tower would have 


12 


reduced the rooms of the circular basement, so that they would only 
have been simple passages. 

The extra thickness proposed for the inclined mass of the staircase 
could only increase the stability of the tower on account of the weight 
it added to it. But, admitting the necessity of this increase of sta¬ 
bility, it might be feared that such a mass of masonry built in an 
inclined position, would eventually prove more hurtful than useful to 
the solidity of the edifice. 

The employment of iron cramps was proposed as a means of pre¬ 
venting the effect of the concussions of nature in leading to the sepa¬ 
ration of the stones in the same course. Now from the observations 
cited above such an effect cannot be feared for the Belle Isle tower, 
which will not be exposed to the shock of the waves like the Eddy- 
stone, Bell Rock, and Le Four light-houses. Besides it is evident 
that this system of cramps, adding nothing to the adhesion of the 
layers to each other, would not sensibly increase the stability of the 
tower against the action of a horizontal force tending to overturn it. 

The arrangement of the two flat arches of the upper rooms of the 
tower appeared subject to some inconveniences, and it has been judged 
proper to substitute iron platforms for them. I will observe with 
regard to this, that it is desirable to avoid the employment of every 
kind of iron work in edifices exposed to the destructive action of sea 
air. I therefore would not hesitate to prefer, in the case in question, 
brick arches to iron platforms. I must acknowledge, however, that 
the renewal of these platforms will present but little difficulty, so that 
my observation here has for its object a question of economy, rather 
than one of art. 

In fine, the modifications of the design of A. Fresnel for the Belle 
Isle light-house definitely adopted, are reduced to the addition of a 
partition wall 1.91 feet thick, having an interior void 4.92 feet in 
diameter, and in the substitution of two iron platforms for the two 
flat arches in the upper part of the tower. 

For the calculations relating to the stability of this edifice, I have 
admitted with the author of the design— 

1. That the point of easiest rupture would be situated at the level of the roof of the 
basement, except in the case where I have left out of consideration the partition walls, 
the rooms of the basement, and the platform which covers them ; 

2. That if the tower were to yield to the effort of the wind, there would be crushing 
over the edge of rotation, so that the arm of lever of the resistance instead of being equal 
to the radius of the section of rupture, that is to 11.45 feet, would be reduced to 9.84 
feet. (4.) 

3. That the cubic yard of masonry of cut granite weighs 4552.5 lbs. 


13 


I have also calculated the additional stability due to the partition 
wall of the modified design, considering this interior tower as making 
one body with the principal tower, at least at the instant which 
would immediately precede the fall of the edifice. In other words, I 
have admitted that the additional stability would be proportional to 
the weight of the partition wall. 

The weight 4552.5 lbs. attributed to the cubic yard of granite 
masonry is perhaps a little large; but I have applied it also to the 
marble of the tower of Boulogne, and I have taken care to take the 
maximum in the determination of the weights of the other edifices 
taken for terms of comparison. 

From these bases, and the mode of calculation which has just been 
explained, I have found for the tower of Belle Isle, considered under 


different hypotheses, the following stabilities : 

1. Design first approved.(5.).... 4.9 

2. With partition wall 0.98 feet thick, and 6.56 feet interior diameter.5.3 

3. With partition wall 1.97 feet thick, and 4.92 feet interior diameter-5.8 

4. With full newell 8.86 feet in diameter, comprising a filling up with rubble 

masonry 4.92 feet in diameter___6.2 

Finally, admitting the suppression of the six partition walls of the basement and 
that of the platform, I have found for the stability of the column, considering 
its whole height.......... 5.2 


Thus then the tower of Belle Isle, finished according to the first 
design, would have presented a stabitity equivalent to nearly five 
times the effort of a storm capable of exerting a pressure of 507 lbs. 
per square yard, and the addition of a partition wall 1.97 feet thick, 
will only increase this stability about one-fourth. 

I am far from despising the facilities for the construction of the 
staircase which the introduction of the partition wall will add, and 
the increase of solidity to this part of the edifice which will result 
from it. But, on the other hand, I will observe with the author of 

(4.) To follow this hypothesis in all its consequences it would be necessary to admit a 
deviation from the vertical of 1.60 feet, and to add to the moment of the pressure of the 
wind the moment of the weight of the masonry beyond the vertical; but we would then 
be too far from the conditions of equilibrium considered at the instant which would 
immediately precede the fall of the tower. 

(5.) Weight of the column above the basement, 983.6 cub yd. X 4552.5 = 4477839 lbs. 

Moment of the horizontal resistance 4477839. X 3.28 = 14687312. 

Moment of the pressure exerted by the wind § X 507 X 8806. = 2976458. 

Eatio of the moments of resistance and pressure, or stability =4.9 







14 


tlie design, that admitting the insufficiency of the penetrations of the 
steps into the wall of the tower to render the stability of each step 
independent of that of the others, we might have, as in the staircase 
of the tower of Cordouan, consolidated the system by landings placed 
at oertain distances. We could thus have prevented the inconveni¬ 
ences arising from fearing the solidity of the 266 steps of the grand 
circular staircase, without sacrificing the happy effect, and the real 
advantages for the service, which the projected system would have 
offered. Moreover, it cannot be denied that these considerations 
ought to have appeared of little importance, when the stability even 
of the edifice has been placed in doubt, and without doubt, it was 
necessary to make some concessions to fears so grave. We remark, 
besides, that in deviating from the combination according to which 
the hollow void of the partition wall would have been filled with 
masonry, we have assured ourselves of the maintenance of an import¬ 
ant advantage, that of being able to raise the building materials in 
the interior of the tower. 

In the comparisons which are to follow, I shall suppose the Belle 
Isle light-house built in conformity with the arrangements definitely 
adopted, so that, when I speak of the stability of this edifice, it must 
be understood that the tower, with the partition wall 1.97 feet thick, 
and having a stability equivalent to 5.8, is refered to. 

Signal tower of L’ Orient. (Fig. 1.) 

The signal tower of L’Orient was constructed in 1785 by M. Guil- 
lois, engineer, upon the highest point in that city, 65.61 feet above 
high water. The edifice presents the form of a truncated cone 
122.56 feet high, 23.44 feet in diameter at the base, reduced to 13.84 
feet in diameter below the capital. 

The staircase with full newell occupies a cylindrical well 11.25 feet 
in diameter. The diameter of the newell is 1 foot. Upon the plat¬ 
form of the tower a room of wood is placed, from the middle of which 
a signal mast is raised. 

The body of the tower is built of rubble masonry, with chain 
courses, plinths, base, and capital of cut granite. This mixed system, 
applied to so elevated an edifice, might entail the greatest inconve¬ 
niences, in spite of the thickness of the masonry, and the great 
inclination of the exterior walls ; but these have been avoided by the 


15 


great care taken in the construction of all parts of this tower. So 
the oscillations which it must experience in tempests have not pro¬ 
duced any fissure neither in the cut stone masonry, nor even in the 
joints of the rubble stone sides. From its base, it towers over all the 
edifices of the city, and on the side towards the sea in the direction of 
the prevailing winds remains entirely unmasked. 

It is evident that the thickness of the masonry might have been 
much reduced, if the edifice could have been entirely constructed of 
cut stone. There would have resulted, it is true, an apparent dimi¬ 
nution of stability with respect to the efforts of the wind, hut the 
unfortunate chances attached to the adoption of the mixed system of 
rubble masonry and chain courses of cut stone would have been 
avoided. 

The effects of unequal settling were much more to he feared for the 
tower of L’Orient as it has been built, than was the action of the 
wind perhaps for that of Belle Isle ; and, in fine, the first structure, 
although superior in horizontal stability, appears bolder to me than 
the second. 

Applying to the tower of L’Orient the method of calculation pre¬ 
viously explained, and taking 4552.5 lbs. for the weight of the cubic 
yard of cut stone masonry, and 3372.3 lbs. for that of a cubic yard of 
rubble masonry we find for its stability 7.4.< 6) So that it only exceeds 
by one-third the stability of the Belle Isle tower. 

We might have expected a much greater difference from a first 
glance at the comparative sections of the two edifices ; but this result 
is easily explained by the ratio between the specific weights of rubble 
and cut stone masonry. 

Liglit-house of Genoa. (Fig. 2.) 

The light-house of Genoa is, after that of Cordouan, the most remark¬ 
able among all those which are exclusively devoted to the lighting of 
seacoasts. It is elevated at the extremity of the promontory of San 
Benigno upon a mass of rocks 128 feet above the level of the sea. Its 

cubic yards. cubic yards. 

(6)Weight of tower r= 167.4 X 4552.5 -f 897.4 X 3372.3 = 3788609 lbs. 

Moment of horizontal resistance 3788609 X 3.379 — 12801709.8. 

Moment of the pressure exerted by the wind $ X 507 X 5110.9 rr: 1727490.9. 

Ratio of the moments or stability r: 7.4. 


1G 


plan is square. It presents the appearance of two towers, one placed 
above the other, the lower 108.92 feet high and 29.53 feet square, 
and the upper 97.77 feet high and 22.97 feet square. The upper 
platform is crowned by a small round tower 11.48 feet high and 20 
feet in diameter, upon which is raised a lantern 11.81 feet in diameter 
and 18.37 feet in height, including a hemispherical dome. The 
thickness of the principal walls is about 6.5 feet in the lower story, 
and about 3.25 feet in the upper story/ 7 ) These two stories are 
divided, the first into four, and the second into three chambers, by 
seven flattened arches. Light wrought iron cramps counteract the 
thrust of these arches, according to the system generally adopted in 
Italy. 

The staircases, disposed laterally, are of light construction, and add 
very little to the stability of the edifice. The steps are formed of 
schistose slabs. 

The masonry, except the cornices and balustrades, is rubble or 
large schistose blocks, with interior revetments of brick in a few 
places only. The exterior walls are covered with a coating of mor¬ 
tar made of lime and sand. 

The success of this great construction must above all things be 
attributed to the excellence of the mortar. And we see that here, the 
most imminent danger does not proceed from the action of the winds, 
but from the more or less regular settling in an edifice where rubble 
masonry for the greater part nearly unwrought, is found piled to a 
height of about 220 feet. 

For the want of precise figures to determine the mean weight of the 
masonry of the Genoa light-house, I have taken the greatest, reckon¬ 
ing 3878.1 lbs. per cubic yard. I have thus found that the absolute 
stability of this light-house may be valued at 6.2. (8) So that it is only 
about one-twelfth above that of the Belle Isle light-house. 

(7) I -will confess that I cannot answer for the exactness of these dimensions. I have 
taken them from a very carefully made drawing (but not numbered) made to a scale of 
belonging to the archives of the commission of light-houses. According to a note of 
Lieut. Col. Chiodo, of the engineers attached to the fortress of Genoa, the first story of 
the large light-house of this city was 113.84 feet high, and the second 109.73 feet high ; 
but it is more than probable that the parapet wall of the lantern is comprised in the 
second height, so that the difference between my estimate and that of Col. Chiodo, is 
reduced to 5.40 feet. 

( 8 ) Weight of the tower 3761.3 cubic yards X 3878.1 — 14586638.C. 

Moment of the horizontal resistance 14586638.6 X 4.92 — 71766264. 

Moment of the pressure exerted by the wind 22636.93 X 507 — 11476923.51. 

Stability = 6.2. 


17 


With respect to the action of the wind, the tower of Genoa may at 
first sight appear placed under more favorable circumstances than the 
Belle Isle tower, which will not be sheltered on any side, whilst the 
first, placed at the foot of the Appenines, is sheltered for more than 
half of the horizon. However, observation appears to weaken this 
first view, for it seems fixed that the sudden storms of the Mediterra¬ 
nean are not at all less violent than the gales of the ocean in the same 
parallel, and sailors who have frequented the river of Genoa agree in 
stating that the sudden gales near mountainous coasts are more 
terrible than those in the open sea. 

Pilier light-house , near the island of Noirmouticr. (Fig- 4.) 

The Pilier light-house, constructed in 1827 by M. Plantier, jr., 
engineer, offers here a most important comparison, for its situation 
upon an isolated rock in the sea, one league from the northeast point 
of the island of Hoirmoutier, appears quite identical, with respect to 
the frequency and intensity of the storms, to that which could have 
been built upon one of the highest plateaus of Belle Isle. This edi¬ 
fice presents the form of a column 86.27 feet high, with a base 15.09 
feet in diameter, reduced to 12.04 feet below the cornice. Upon the 
platform is a cylindrical parapet wall 5.91 feet high, and 11.35 feet 
in diameter. It is surmounted by a lantern 9.84 feet in diameter, 
and 12.14 feet high, including a dome 3.75 feet high. The winding 
staircase with full newcll occupies a cylindrical well G.5G feet in 
diameter and G5.61 feet high. 

A square building of light construction surrounds the foot of the 
tower. It is 45.28 feet square and 9.84 feet high, the roof, which is 
covered with tiles, not included. Four partition walls 1.31 foot thick, 
join three of the faces of the building to the body of the tower. 

The thickness of the wall of this tower is 4.26 feet at the level of 
the grouud, and is reduced to 2.95 feet at the top of the staircase. 
At this level there is an interior offset of 0.G6 foot, and at 9 84 feet 
above, a second offset of 0.16 foot. 

The interior space corresponding to the capital is occupied by a 
service chamber comprised between two iron platforms. Between the 
beams upon which the upper platform rests have been placed six ribs 
of a cast iron arch, in the key of which is fixed the support of the 
frame of a revolving lens apparatus. 

L. H—3 


18 


The principal part of the body of the tower for a height of 65.61 
feet has been built with cut granite for the exterior, with an interior 
mass of rubble. The upper part is built entirely of cut granite. 

I have supposed that the point of easiest rupture was situated 13.12 
feet above the ground, and I have found that the stability of the 
Pilier tower may he represented by the number 4.4 (9) 

Thus the stability of the Belle Isle light-house would exceed more 
than one-fourth that of the Pilier light-house, which has never been 
questioned. Now, admitting that there was an equality between the 
two edifices with regard to their resistance to the wind, there would 
still remain an important advantage in favor of the first, on account 
of its construction being much more homogeneous. I was in the 
Pilier light-house some months after its completion, during a storm 
which lasted several days and imparted an oscillating movement 
upon the tower, very light without doubt, but which gave one an 
irresistible impulse to suppport oneself against the side of the upper 
chamber. Since that time the same edifice has borne much more 
violent tempests, and no fissure has been shown in any of the masonry 
up to the present time. 

Planter Light-house near Marseilles. (Fig. 5.) 

The light-house constructed in 1827 upon the Planier rock at the 
entrance of the roadstead of Marseilles, has presented several circum¬ 
stances interesting to study, but upon which I shall not enlarge, 
except when they appear to me to be attached to the special object of 
this memoir. 

According to the design suggested in 1823, by M. Garella, engi¬ 
neer in chief, director, the Planier light-house was to be constructed 
as a round tower 69.87 feet high, raised upon a rectangular base¬ 
ment 26.25 feet high and 45.93 feet square. The tower or column 
was to have a diameter of 17.71 feet at its foot. A circular well-room 
8.53 feet in diameter was reserved for a winding staircase with full 

(9) Weight of the tower = 219.91 cubic yards X 4552.5 -|- 74.88 cubic yard X 3372.3 = 
1253686.426 lbs. 

Moment of the horizontal resistance 1253686.426 X 2.19 = 2745573.27. 

Moment of the pressure exerted by the wind = 1837.61 X | X 507 = 621112 18. 

Stability = 4.4. 


19 


newell, so that the wall of the column was to be 4.59 feet thick at its 
base. The basement was solid as high as the level of the first floor, 
9.84 feet above the rock, and contained several rooms covered with 
semi-circular cylindrical arches respectively parallel to the four walls 
of the enclosure, forming piers 3.28 feet thick. These arches, 9.84 
feet in diameter, raised upon piers 11.15 feet high, were to be .98 foot 
thick at the key, the paving of the roof not included. 

The column was to be crowned by a lantern 11.15 feet in diameter 
and 11.48 feet high, covered with a conical roof 3.28 feet high. 

The exterior wall and the exterior staircases of the basement, as 
well as the coping of the cornice, were to be built of hard cut stone. (10) 

The exterior of the column and its staircase were designed of a 
very tender limestone, and the remainder of the masonry, except the 
brick arches of the basement, was to be of rubble or large blocks. 

The work was commenced according to these arrangements, and 
the basement was finished, when, in the month of March, 1825, the 
commission of light-houses, taking into consideration the importance 
of the part which the Planier light-house was to play among all those 
which it was proposed to light on our Mediterranean coast, decreed 
that the height of the tower should be made 131.22 feet. 

M. Garella consulted on the subject, and appreciating all the ad¬ 
vantage of extending the range of the light, believed that he might 
consent to the change without essentially modifying the economy of 
his design, and the construction was consequently carried on in con¬ 
formity with the new programme. 

It appears that the works presented no circumstance of note until 
the winter of 1827. At that time, fissures, and indications of settle¬ 
ment, began to be shown at the foot of the staircase, and were attribu¬ 
ted in part to the oscillations impressed upon the tower by a succes¬ 
sion of very violent gales. These damages were increased by an 
extraordinarily violent storm, which took place on the 18th of March 
of the same year. 

According to the observations collected by M. Cousinery, engineer, 
the wind had caused the shaft of the tower to oscillate like an elastic 
rod, and its oscillations had produced openings or cracks in the cylin¬ 
drical arches of the rooms of the basement, and several ruptures in 

(10 )Magnesian limestone from the quarries of Cassis, near Ciotat, and of the same nature as 
the Planier rock. 


20 


the lower part of the staircase. The upper part of the edifice pre¬ 
sented no trace of separation. 

I will observe that the increase of height of the tower had pru¬ 
dently been limited to 16.40 feet, and that at the time these damages 
were discovered, the lantern had not yet been placed, or at any rate 
had not been glazed. 

The engineer-in-chief caused the works to he suspended, and pre¬ 
sented a design of supplemental works, which has been as well 
executed as it was happily conceived. In conformity with this addi¬ 
tional design, all the empty spaces of the lower basement were filled 
with masonry for a height of 14.76 feet, except a circular space 6.56 
feet in diameter, reserved near the entrance door for a winding stair¬ 
case. The principal staircase was also filled up for a height of 27.23 
feet, and the foot of the tower was made solid 18.04 feet high above 
the first square mass by a second mass 23.95 feet square, in which 
was placed a staircase communicating with that of the tower. A 
second basement, 39.37 feet square and 14.43 feet high, was raised 
above the first, and divided into several rooms and store-rooms. 

The glazing of the lantern was only placed near the end of 1828, 
and the lighting apparatus, placed a short time afterwards, was set 
in operation March 1, 1829. 

As a last result, no other trace of damage to the Planier light-house 
was noticed, except a very light inclination of the shaft of the column, 
and this edifice appears now perfectly consolidated. It can he seen, 
too, from an inspection of Jig. 5, that the addition of a second story to 
the basement detracts in no degree from the happy architectural 
effect of the primitive design. 

The study of the facts that I have just pointed out is the more in¬ 
teresting as they appear to have given rise to erroneous consequences, 
which, perhaps, have not been without influence upon the arrange¬ 
ments adopted for some of the light-houses recently designed. 

The design originally approved for the Planier light-house was 
conceived in a system of rigid economy, which, without excluding 
elegance of proportions, could only suit a tower of moderate height. ( n > 

(ll) It is to be remarked that notwithstanding the importance of the additional works 
executed at the Planier light-house, this monument, elevated upon a rock situated three 
leagues at sea and often inaccessible, has only cost 70.000 frcs. This is scarcely one-third 
of what a similar edifice would have cost in an analogous situation upon the coast of the 
Atlantic. 


21 


In the first rank of the circumstances which might render the increase 
of height dangerous, I will cite the small tenacity of the rock 
employed in the construction of the principal staircase and exterior 
of the column. As well as I have been able to judge from a simple 
inspection, this rock could by no means sustain without crushing or 
splitting, the increased pressure which the oscillations of the column 
would suddenly bring upon some parts of the lower courses. Hence, 
the effect of these oscillations would he rapidly increased, particularly 
at a time when the interior mass of rubble masonry made with com¬ 
mon lime had acquired very little consistency. 

It is probable that if the mortar had been hardened when the edi¬ 
fice experienced a succession of violent gales, the damage would have 
been much less severe. Nevertheless I have been led to believe that 
the arches of the basement, with regard to their arrangement and 
lightness, in any event, would have suffered some rupture in conse¬ 
quence of the oscillations of the tower. 

I will here remark, in this connection, that the design of the Belle 
Isle light-house presents more security, since the system of conoidal 
arches of its basement exercises no thrust against the exterior wall. I 
will further remark, that admitting that the Belle Isle tower, as it 
was designed by A. Fresnel, were bent 1.97 feet in tempests, the cor¬ 
responding deviation of the platform would have been only 0.06 
inches. (12) 

The Planier tower, according to what has just been said, has passed 
through two states essentially different, which it is important to com¬ 
pare with respect to the stability. 

In its first state, before the execution of the additional works, this 
edifice presented above the basement a column 86.93 feet high, not 
yet surmounted with its lantern. Its stability was then about 5.3. 

(12) Knowing the total flexion of an elastic rod uniformily pressed along its whole 
length, we can deduce its deviation at any point whatever by the equation : 

* = P ( * k + * y * ) 

in which h represents the height of the rod, and <5 the deviation of its summit. (See the 
Memoir of M. Duleau upon the Resistance of Iron.) 

If we consider the Belle Isle tower as an elastic rod 186.99 feet high, having an extreme 
deviation & = 1.97 feet, and make y equal to the ordinate of the platform of the base¬ 
ment, that is to say, 31.17 feet, we will have for the deviation at the level of that 
platform— 

x — 0.06 inches. 


Si 

4 


* 


22 


At present, the column of Planier is only 71.35 feet high above the 
raised basement, but it is surmounted with its large lantern, and its 
stability is reduced to 4.6. (13) 

This singular result, which I had foreseen before I was able to col¬ 
lect all of the documents necessary to verify it by calculation, confirms 
the views I have just presented upon the different causes of the 
damage experienced in the construction of the Planier tower. In fact, 
if the damage had only been caused by the insufficiency of the weight 
of the masonry of the tower, the additional works would have in no 
degree attained their end, since the column topped with its lantern 
has been found, notwithstanding the reduction of the height of its 
shaft, to have lost more than one-eighth of its original stability. 
But independent of the gradual hardening of the mortar, which has 
sensibly increased the elastic force of this column, the crushing of the 
lower courses of the tower has been arrested by the masonry filling of 
the basement rooms, whence it has resulted that the edifice, although 
less stable at present, at least in appearance, has in fact gained a 
great deal in solidity. 

The stability of the Belle Isle tower, according to the results given 
above, would only exceed about one-fourth the present stability of the 
Planier tower ; but taking into account the great difference which the 
nature of the materials and the system of construction of the two 
edifices presents, I think it superfluous to stop for the annoying infer¬ 
ences to which this comparison might give rise. 

Column of Boidogne-sur-mer. (Fig. 6.) 

The triumphal column of Boulogne-sur-mer is, among the high 
towers exposed to frequent gales, one of the boldest which exist in 

(IS)First state of the tower .—The weight of the masonry of tender limestone, and of rubble 
of moderate sized stones, it has appeared to me ought not to be valued at more than 
3372.3 lbs. per cubic yard ; hence, for 451.52 cubic yards 1522661 lbs. 

Moment of horizontal resistance 1522661 X 2.53 — 3862332.33. 

Moment of the pressure exerted by the wind § X 507 X 2133.49 — 721119.62. 

Stability — 5.3 

Present state of the toicer .—"Weight of the masonry— 350.02 cub. yd. X 3372.3 = 1180372.45. 

Moment of the horizontal resistance = 1180372.45 X 2.44 = 2880108.78. 

Moment of the pressure exerted by the wind § X 507 X 1850.5 = 625469. 

Stability = 4.6. 

Without its lantern, the Planier tower, in its present state, would have a stability 
equivalent to 6.0. 


23 


France. It is raised to a lieiglit of 167.54 feet, upon a plain about 
160 feet above the level of the highest tides. 

The total height of this monument is divided as follows : 


1. Pedestal and its base_____ 32.05 feet. 

2. Base of the column____ 6.99 “ 

3. Shaft.. 92.68 “ 

4. Capital.—------ 10.32 “ 

5. Parapet, &c _____ 25.50 “ 


Total as given above________167.54 “ 


A glance at the section,^. 6, is sufficient to show that the point of 
easiest rupture corresponds to the foot of the shaft, so that the part to 
consider with respect to the resistance to the action of the wind only 
comprises a height of 135.48 feet. 

The mean exterior diameter of the shaft of the tower is 13.25 feet. 
In the interior is a winding staircase, with solid newell, in a well 7.15 
feet in mean diameter. The diameter of the newell is 2.78 feet. 

The whole of the masonry is of the choicest marble of Lunel. The 
shaft is divided into horizontal courses 2.65 feet rise, composed alter¬ 
natively of four and eight pieces joined by wrought iron clamps 1.97 
foot long by .083 foot thick. Each course corresponds to five steps, 
cut with their newell from a single block of stone, which engages 0.10 
foot in the wall of the circular well. 

The mortar of excellent quality, was made of Boulogne lime and 
cement of tiles. 

The stability of this edifice, calculated on the same basis as that 
adopted for the Belle Isle tower, is only 3.5 (14) 

Thus the stability of the Belle Isle tower would exceed that of the 
tower of Boulogne two-thirds. 

This comparison must appear conclusive in favor of the design 
adopted for the Belle Isle light-house, since the two edifices compared 
are both of conical form, they are both composed of cut stone without 
mixture of rubble masonry, and are both elevated upon plateaux 

( 14 ) Weight of the masonry 412.28 cub. yds. X 4552.5 rr 1876904.7. 

Moment of the horizontal resistance 1876904.7 X 1.91 rr 3584887.98. 

Moment of the pressure $ X 507 X 2991.07 1010981.66. 

Stability — 3.54. 

Supposing all the voids filled, the stability of the tower of Boulogne would still be 
only 4.6. 









24 


equally exposed to the action of the winds. It is true, the joints are 
much less numerous in the column of Boulogne ; hut the great rise of 
the courses, although certainly favorable to the solidity of their system, 
would have no influence against a horizontal effort sufficient to over¬ 
turn it. In this respect the employment of iron cramps for the stones 
of the same course appears to me to be nearly useless, and only justi¬ 
fied if the question was to resist the shaking caused by the shock of a 
hard body, or the shocks of waves. To increase in an efficient man¬ 
ner the resistance of such an edifice against the pressure of the wind 
by the use of iron, it would have been necessary to bind the courses 
together by means of anchors which would run through several 
courses. However, this excess of expensive precautions is entirely 
superfluous. In fact, it appears from researches that I owe to the 
kindness of M. Marguet, chief engineer of the port of Boulogne, that 
the column of Boulogne presents not the slightest trace of fissure, 
whence it must be concluded that the severest storms that it has 
experienced so far have in no degree compromised its stability. I 
will add, from the authority of several experienced mariners, that the 
plateau of Boulogne is exposed to gales no less violent than those 
which the Belle Isle liglit-house must bear. 

Chimneys of the salt refinery of Ars, Jig. 7 ; of the forges of Alais, Jig. 8 ; of the steam 
engine of the dock of St. Ouen, Jig. 9 ; and of the gas factory of the Faubourg Montmartre) 
Jig. 10. 

The five edifices which have been discussed are all situated in 
localities analogous to that of Belle Isle, as to the intensity of the 
action of the wind. It remains for me to speak of four high chimneys, 
only one of which is in truth exposed to gales from the sea, but the 
three others, although situated in the interior, nevertheless offer 
remarkable results by their comparison with the tower of Belle Isle. 

I will cite, in the first place, the brick chimney of the salt refinery of 
the village of Ars, Isle of Be. 

This chimney is of quadrangular shape, 89.76 feet high, 11.28 feet 
square at the base, and 4.49 feet square at the top. The thickness of 
the walls is 2.92 feet at the base, and is reduced to 1.48 foot at the 
top by four offsets of 0.36 foot each. The chimney of Ars is con¬ 
tained in the building of the refinery about 30 feet, so that it is only 
subjected to the action of the wind above this height. It was built in 
1825, and it appears from authentic documents collected by M. Potel, 


25 


civil engineer at La Rochelle, that since that time the island of Re 
has experienced several remarkably violent gales, the action of which 
is fully developed against an edifice wholly unmasked on all sides. 

If we admit that the section of easiest rupture corresponds to the 
level of the ceiling of the refinery, and that a cubic yard of brick 
work weighs 2529 pounds, we will find for the stability of the chimney 
of Ars 1.66. ( 15,) So the stability of the Belle Isle light-house would 
be equal to 3^ times that of this chimney—a result no less decisive 
than that which the Pilier light-house has furnished. 

I will cite, in the second place, the chimney of the forges and 
foundries of Alais, department of the G-ard. From a design, and 
different accounts, the communication of which I owe to the kindness 
of M. Berard, director-general of bridges and roads and of mines, 
this chimney, which, according to the design, was to have been 
195.86 feet high, has only been built 180.43 feet high. Its form is a 
truncated cone, the two bases of which are respectively 20.99 feet 
and 7.70 feet in diameter. The thickness of its circular wall is 4.92 
feet at the base, and is reduced to .81 foot at the top. Four offsets 
have been made in the interior face of the wall. The first offset is 
1.08 foot, and is made at a height of 48.88 feet. The three others 
are 0.41 foot each, and are made every 32.80 feet. The space com¬ 
prised between the ground and the first offset is cylindrical, so that 
the thickness of the wall is variable through that height, but for the 
remainder of the height of the shaft the interior faces are parallel to 
the exterior ones. 

This chimney is built of brick, except a base 9.84 feet high, which 
is built of cut stone. 

It is easy to assure ourselves, by a preliminary approximate calcu¬ 
lation, that the point of easiest rupture is situated just above the mass 
of cut stone, so that, with reference to stability, we have only to 
consider the part constructed of bricks. 


(15-) Moment of the resistance 113.97 cubic yards X 2529 X 1.64 — 472680.8. 

Moment of the pressure exerted by the wind 23.23 X 2.38 X 10.23 X 507 = 282604.8. 
Stability = 1.66. 

I have supposed, to simplify the calculation, the chimney unmasked to the level of the 
ceiling, which does not sensibly affect the value of the stability that would have been 
found considering only the part above the roof. 

L. H.—4 


26 


Admitting, as in the preceding article, that a cubic yard of brick¬ 
work weighs 2529 pounds, I have found the stability of this chim¬ 
ney equivalent to 1.76. (l6 ) 

Thus it does not attain the one-third of the stability of the Belle 
Isle light-liouse. 

The chimney of the forges of Alais, being of recent construction, 
has probably not yet sustained the maximum of effort to which it 
may be exposed by the action of the winds ; but it is to be presumed 
that this last proof will not be waited for long, as all of the eastern 
part of Languedoc annually experiences tempests which are of extreme 
violence. This edifice is, besides, completely isolated and unmasked, 
and the gales which it has borne during two equinoxes have not 
occasioned the slightest fissures in the masonry. 

The chimney of the steam engine of the dock of St. Oaen is also of 
recent construction ; but it is isolated in a plain where storms of great 
severity occur, and it offers a remarkable example of a construction 
truly bold. 

Its total height is 133.19 feet, a pedestal of 1.97 foot in height 
included. It is a quadrangular truncated pyramid, 10.17 feet square 
above the base, and 3.61 feet square at the foot of the cornice. 

The thickness of the wall is 2.46 feet at the level of the base, 
reduced to 0.82 foot at the top by five offsets at every 21.32 feet. 

The base is built of hard cut stone. The body of the chimney is of 
brick, and the capital is a single piece of cast iron, weighing 2205 
pounds. 

From these given quantities, I have found that the stability of the 
chimney of the steam engine of St. Ouen can be represented by 
0.87. (17) That is, the moment of the horizontal resistance of this 
edifice is inferior to the moment of the pressure which I have con¬ 
sidered as representing the maximum of the force of the wind. 

Tlius, leaving out of consideration the adhesion of the mortar in 

(16) Moment of the resistance, 519.28 cub. yd. X 2529 X 2.9 3808450.1. 

Moment of the pressure exerted by the wind = § X 507 X 205.15 X 24.09 = 2158962.7. 

Stability = 1.76. 

If the chimney of the forges of Alais had been raised to the height originally designed, 
its stability would have been reduced to 1.60. 

(17) Moment of the resistance (184.04 cub. yd. X 2529 -f- 2205.5) X 1.7 = 794992.42. 

Moment of the pressure exerted by the wind, 1798.63 X 507 = 911805.4. 

Stability = 0.866. 


27 


the whole extent of the section of rupture, it must be acknowledged 
that a storm exerting a pressure of 507 pounds per square yard, upon 
one of the faces of the chimney in question, would infallibly overturn it. 
Hence, when it shall have borne without accident the action of the most 
violent winds which are ever experienced in our country, it will be 
demonstrated that this pressure may he considered greater than the 
maximum effort of our hurricanes. We see, besides, from this same 
result, that the stability of the chimney of the dock of St. Ouen is 
not equal to one-sixth of the stability of the Belle Isle light-house. 

To reproduce an example cited by the author of the design of that 
light-house, I have considered that I ought to complete these compar¬ 
isons by the determination of the stability of the chimney of the gas 
factory of the Faubourg Montmartre, situated upon one of the highest 
points in Paris. 

This chimney, built of brick, is 85.29 feet high above the point of 
easiest rupture ; a basement 13.12 feet high not included. 

It presents the form of a square truncated pyramid, 8.20 feet square 
at the base, and 4.92 feet square at the top. The thickness of the 
wall diminishes from 1.64 foot to 0.82 foot, by means of the two 
offsets, each 0.41 foot. 

I have found that the stability of this edifice may be represented 
by 0.71 . (18) So that it scarcely attains one-eighth of the stability of 
the Belle Isle tower. 


Conclusion. 

The results of the calculations and comparisons that I have pre¬ 
sented may be shown in the following table, where the numbers ex¬ 
pressing the absolute stabilities of the edifices are placed by the side 
of those expressing the relative stabilities, calculated by taking the 
stability of the tower of Belle Isle for a unit. 


(13)Moment of the resistance 85.02 cubic yards X 2529 X 1-36 = 292352.4. 

Moment of the pressure exerted by the wind 63.27 square yard X 12.97 X 507 = 416039. 

Stability = 0.71. 


4P 


28 


Stabilities. 


Absolute. Relative. 


Signal tower of L’Orient. Fig. 1..--- 7.4 1.28 

Light-house of Genoa. Fig. 2-....- 6.2 1.07 

Light-house of Belle Isle (with partition wall 1.97 foot thick.) Fig. 3 5.8 1.00 

Light-house of the Pilier (near Noirmoutier island. Fig. 4- 4.4 0.76 

Light-house of Planier (near Marseilles.) Fig. 5_ 4.6 0.79 

Column of Boulogne. Fig. 6- 3.5 0.60 

Chimney of the salt refinery of Ars. Fig. 7_ 1.64 0.28 

Chimney of the forges and foundries of Alais, (Gard.) Fig. 8- 1.76 0.30 

Chimney of the steam engine of the dock of St. Ouen. Fig. 9- 0.87 0.15 

Chimney of the gas factory of the Faubourg Montmartre. Fig. 10. 0.71 0.12 


This table, joined to the comparison represented on the plate, 
appears to me to offer a superabundance of proofs which ought to 
dispel all doubts raised upon the stability of the Belle Isle light¬ 
house, as to the resistance which it should oppose to the efforts of the 
wind. 

Of the nine edifices taken for terms of comparison, two, it is true, 
the tower of L’Orient and that of Genoa, presents a stability superior 
to that of this light-house, and a third, the Planier tower, has been 
somewhat damaged ; but the very economical system of their con¬ 
struction is so inferior in true solidity to that of the tower designed 
for Belle Isle, that these three comparisons cannot weaken the conse¬ 
quences resulting from the other terms of comparison. I will even 
add that the example drawn from the two first edifices must appear 
very encouraging, since they are but little superior in horizontal 
resistance to that tower, and their long and perfect preservation 
shows an evident excess of stability. 

The tower of Boulogne, superior to that of Belle Isle in nicety of 
cutting, is otherwise so inferior in horizontal resistance, that this 
single example may appear sufficient to decide the question. (19) 

The Pilier light-house, inferior to that of Belle Isle with respect 
both to stability and the system of construction, offers a comparison 
to which there is only wanting to make it as conclusive as that of 
the column of Boulogue, the guarantees resulting from a longer proof. 


(19) M. Lamblardie, in his report to the general council of bridges and roads upon differ¬ 
ent modifications of the approved design of the Belle Isle light-house proposed by the 
engineers charged with its execution, has insisted particularly upon the consequences 
resulting from the comparison of this design with the tower of Boulogne. 











29 


It might be objected that these same guarantees are also wanting in 
the examples drawn from the brick chimneys of Ars, Alais, St. Ouen, 
and the Faubourg Montmartre, and that, besides, three of these chim¬ 
neys are situated in localities where the wind does not blow with the 
same violence as at Belle Isle. It maybe answered as to the objection 
founded on the fact that these four edifices have not long existed, that 
England has contained, for more than twenty years, a considerable 
number of chimneys as light as these, which have served as models 
for constructions of this kind executed in France. I will agree that 
the localities where they are situated are generally less exposed to the 
wind than the high plateaux of Belle Isle, hut I am firmly of the 
belief that the real intensity of the winds which prevail at sea is ex¬ 
aggerated by confounding their frequency with their violence. At the 
surface of the sea, the motions of the lower layers of the atmosphere 
are propagated, it is true, with more facility and uniformity than upon 
land, hut it does not follow that tempests are always more violent on 
the sea than on the land, or in other words, that any point whatever 
of the continents cannot experience in a longer or shorter interval 
hurricanes quite as terrible as any point whatever of the surface of 
the sea situated under the same parallel. The frequent examples of 
trees broken down or torn up in the interior of the country prove what 
energy the wind can develop there. Doubtless, cases of masonry 
edifices thus overturned are a great deal more rare. As I have al¬ 
ready observed, it is to unequal settling resulting from a bad estab¬ 
lishment of the foundations, to a defect in homogenity and bond of the 
masonry, or to a defect in the resistance of the materials, that must be 
attributed nearly the whole of the damages sustained by edifices of 
great elevation. It therefore would be vain to increase their apparent 
stability, if their system of construction was essentially vicious, or if 
the workmanship was neglected. But none of these causes of destruc¬ 
tion or of damage appear to be feared for the Belle Isle light-house, 
founded upon an incompressible soil and designed to be entirely of 
cut stone, and it cannot be doubted that the success of its construction 
will be fully assured by an active superintendence and a continual 
exaction of the execution of the clauses of the specifications. 


THE END. 






















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